In mathematics, the radical symbol, radical sign, root symbol, radix, or surd is a symbol for the square root or higher-order root of a number. The square root of a number x is written as
while the nth root of x is written as
It is also used for other meanings in more advanced mathematics, such as the radical of an ideal.
In linguistics, the symbol is used to denote a root word.
Each positive real number has two square roots, one positive and the other negative. The square root symbol refers to the principal square root, which is the positive one. The two square roots of a negative number are both imaginary numbers, and the square root symbol refers to the principal square root, the one with a positive imaginary part. For the definition of the principal square root of other complex numbers, see Square root § Principal square root of a complex number.
The origin of the root symbol √ is largely speculative. Some sources imply that the symbol was first used by Arab mathematicians. One of those mathematicians was Abū al-Hasan ibn Alī al-Qalasādī (1421–1486). Legend has it that it was taken from the Arabic letter "ج" ( ǧīm ), which is the first letter in the Arabic word "جذر" (jadhir, meaning "root"). [1] However, Leonhard Euler [2] believed it originated from the letter "r", the first letter of the Latin word "radix" (meaning "root"), referring to the same mathematical operation.
The symbol was first seen in print without the vinculum (the horizontal "bar" over the numbers inside the radical symbol) in the year 1525 in Die Coss by Christoff Rudolff, a German mathematician. In 1637 Descartes was the first to unite the German radical sign √ with the vinculum to create the radical symbol in common use today. [3]
The Unicode and HTML character codes for the radical symbols are:
| Read | Character | Unicode [4] | XML | URL | HTML [5] |
|---|---|---|---|---|---|
| Square root | √ | U+221A | √ or √ | %E2%88%9A | √ or √ |
| Cube root | ∛ | U+221B | ∛ or ∛ | %E2%88%9B | |
| Fourth root | ∜ | U+221C | ∜ or ∜ | %E2%88%9C |
However, these characters differ in appearance from most mathematical typesetting by omitting the overline connected to the radical symbol, which surrounds the argument of the square root function. The OpenType math table allows adding this overline following the radical symbol.
Legacy encodings of the square root character U+221A include:
The Symbol font displays the character without any vinculum whatsoever; the overline may be a separate character at 0x60. [13] The JIS, [14] Wansung [15] and CNS 11643 [11] [16] code charts include a short overline attached to the radical symbol, whereas the GB 2312 [17] and GB 18030 charts do not. [18]
Additionally a "Radical Symbol Bottom" (U+23B7, ⎷) is available in the Miscellaneous Technical block. [19] This was used in contexts where box-drawing characters are used, such as in the technical character set of DEC terminals, to join up with box drawing characters on the line above to create the vinculum. [20]
In LaTeX the square root symbol may be generated by the \sqrt macro, [21] and the square root symbol without the overline may be generated by the \surd macro. [22]
Big-5 or Big5 is a Chinese character encoding method used in Taiwan, Hong Kong, and Macau for traditional Chinese characters.
ISO/IEC 2022Information technology—Character code structure and extension techniques, is an ISO/IEC standard in the field of character encoding. It is equivalent to the ECMA standard ECMA-35, the ANSI standard ANSI X3.41 and the Japanese Industrial Standard JIS X 0202. Originating in 1971, it was most recently revised in 1994.
Shift JIS is a character encoding for the Japanese language, originally developed by the Japanese company ASCII Corporation in conjunction with Microsoft and standardized as JIS X 0208 Appendix 1.
Extended Unix Code (EUC) is a multibyte character encoding system used primarily for Japanese, Korean, and simplified Chinese (characters).
GB/T 2312-1980 is a key official character set of the People's Republic of China, used for Simplified Chinese characters. GB2312 is the registered internet name for EUC-CN, which is its usual encoded form. GB refers to the Guobiao standards (国家标准), whereas the T suffix denotes a non-mandatory standard.
The Chinese Character Code for Information Interchange or CCCII is a character set developed by the Chinese Character Analysis Group in Taiwan. It was first published in 1980, and significantly expanded in 1982 and 1987.
The CNS 11643 character set, also officially known as the Chinese Standard Interchange Code or CSIC, is officially the standard character set of Taiwan. In practice, variants of the related Big5 character set are de facto standard.
The C0 and C1 control code or control character sets define control codes for use in text by computer systems that use ASCII and derivatives of ASCII. The codes represent additional information about the text, such as the position of a cursor, an instruction to start a new line, or a message that the text has been received.
JIS X 0201, a Japanese Industrial Standard developed in 1969, was the first Japanese electronic character set to become widely used. The character set was initially known as JIS C 6220 before the JIS category reform. Its two forms were a 7-bit encoding or an 8-bit encoding, although the 8-bit form was dominant until Unicode replaced it. The full name of this standard is 7-bit and 8-bit coded character sets for information interchange (7ビット及び8ビットの情報交換用符号化文字集合).
む, in hiragana, or ム in katakana, is one of the Japanese kana, which each represent one mora. The hiragana is written with three strokes, while the katakana is written with two. Both represent.
Symbol is one of the four standard fonts available on all PostScript-based printers, starting with Apple's original LaserWriter (1985). It contains a complete unaccented Greek alphabet and a selection of commonly used mathematical symbols. Insofar as it fits into any standard classification, it is a serif font designed in the style of Times New Roman.
KPS 9566 is a North Korean standard specifying a character encoding for the Chosŏn'gŭl (Hangul) writing system used for the Korean language. The edition of 1997 specified an ISO 2022-compliant 94×94 two-byte coded character set. Subsequent editions have added additional encoded characters outside of the 94×94 plane, in a manner comparable to UHC or GBK.
KS X 1001, "Code for Information Interchange ", formerly called KS C 5601, is a South Korean coded character set standard to represent Hangul and Hanja characters on a computer.
Code page 895 is a 7-bit character set and is Japan's national ISO 646 variant. It is the Roman set of the JIS X 0201 Japanese Standard and is variously called Japan 7-Bit Latin, JISCII, JIS Roman, JIS C6220-1969-ro, ISO646-JP or Japanese-Roman. Its ISO-IR registration number is 14.
IBM code page 949 (IBM-949) is a character encoding which has been used by IBM to represent Korean language text on computers. It is a variable-width encoding which represents the characters from the Wansung code defined by the South Korean standard KS X 1001 in a format compatible with EUC-KR, but adds IBM extensions for additional hanja, additional precomposed Hangul syllables, and user-defined characters.
IBM code page 936 is a character encoding for Simplified Chinese including 1880 user-defined characters (UDC), which was superseded in 1993. It is a combination of the single-byte Code page 903 and the double-byte Code page 928. Code page 946 uses the same double-byte component, but an extended single-byte component.
The ISO 2033:1983 standard defines character sets for use with Optical Character Recognition or Magnetic Ink Character Recognition systems. The Japanese standard JIS X 9010:1984 is closely related.
Volume 1 of the Association of Radio Industries and Businesses (ARIB) STD-B24 standard for Broadcast Markup Language specifies, amongst other details, a character encoding for use in Japanese-language broadcasting. It was introduced on 1999-10-26. The latest revision is version 6.3 as of 2016-07-06.
GB 12345, entitled Code of Chinese ideogram set for information interchange supplementary set, is a Traditional Chinese character set standard established by China, and can be thought as the traditional counterpart of GB 2312. It is used as an encoding of traditional Chinese characters, although it is not as commonly used as Big5. It has 6,866 characters, and has no relationship nor compatibility with Big5 and CNS 11643.
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